I get this with my Navy Federal card. I dont have any "prestige" cards but I'd be surprised if anyone got more attention for them than I get for my standard issue NF debit.
I've noticed this too. I'm not actually in the military, but my grandfather was a doctor in the Navy and apparently we've been (literally) grandfathered in for perpetuity. The card has raised eyebrows in places I would not have imagined it would be noticed.
That's almost exactly my situation. My dad was in the Army, so I'm grandfathered in, as well as anyone in my immediate family.
Only somewhat relatedly, The content of the constant ASAA ads during sporting events on TV strikes me as indirect but blatant military propaganda.